Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<cstdio>
using namespace std;

int main() {
	int a;
	cin >> a;
	double MAX = 0;
	int b[1000];
	for (int c = 0; c < a; c++)cin >> b[c];
	sort(b, b + a);
	for (int d = 0; d < a-1; d++) {
		for (int e = d+1; e < a; e++) {
			double sum = 0, k = 0;
			for (int f = a - 1; f != -1; f--) {
				if (f != d&&f != e) {
					sum += b[f];
					k++;
					if (k == 2)break;
				}
			}
			MAX = max(MAX, sum / abs(b[d] - b[e]));
		}
	}
	printf("%.10lf\n", MAX);
}